Learn Hardcore Korean: yeonhyu saebyeogeneun doroga wiheomhanikka cheoncheonhi ga. - Since roads are dangerous at dawn during long weekends, go slowly.

천천히: “slowly, at an easy/careful pace” and is what you naturally say to a person as advice: 천천히 가/하세요.
느리게: “slowly” in a more descriptive/speed sense; common in narration: 차가 느리게 간다. As a command to a person, 느리게 가 is less idiomatic than 천천히 가 .

Breakdown of yeonhyu saebyeogeneun doroga wiheomhanikka cheoncheonhi ga.

What exactly do the parts 연휴, 새벽, and 에는 mean here?

연휴: a span of consecutive holidays (long weekend/holiday period).
새벽: pre-dawn/early morning, roughly from after midnight until around sunrise.
에는: combination of the time/location particle 에 (“at/on/in”) plus the topic/contrast marker 는. Together, 새벽에는 means “as for (at) dawn,” often with a contrastive or generalizing nuance.

Why use 에는 instead of just 에?

Adding 는 topicalizes and often contrasts that time frame with others.

연휴 새벽에 = at dawn during the holiday (neutral).
연휴 새벽에는 = as for dawns during the holiday (implies contrast/emphasis: that time in particular).

Can I say 연휴의 새벽에는 or contract it to 연휴 새벽엔?

연휴의 새벽에는 is grammatically fine but feels more formal/bookish. In everyday speech, Koreans often drop 의 and use the noun-noun sequence: 연휴 새벽에는.
The colloquial contraction 에는 → 엔 is common in speech: 연휴 새벽엔.

Why is it 도로가 with the subject marker 가, not 도로는?